Mathematical model of geomembrane stress-strain curves with a yield peak

Abstract

A simple mathematical model is proposed to describe the stress-strain curves of geomembranes, such as high-density polyethylene (HDPE) geomembranes, that exhibit a yield peak in a uniaxial tensile test. This model is useful for the design of geomembrane applications because it provides an analytical relationship between stresses and strains that can be used in design equations and computer programs. The model consists of an n-order parabola, with the exponent, n, constant or variable as a function of the strain. It has been calibrated with results of uniaxial tensile tests conducted with smooth HDPE geomembranes. If n is a constant (typically n = 4 ), the discrepancy between experimental stress-strain curves and the n-order parabola with a constant exponent is less than 10–15%, which is acceptable in many applications. When more precision is needed, an n-order parabola with a variable exponent can be used. Calculations are then more complex, but the discrepancy between experimental and theoretical stress-strain curves is then less than 3%. This study provides interesting information on the geomembrane modulus. Tests show that the initial modulus of HDPE geomembranes is approximately four times the secant modulus between the origin of the stress-strain curve and the yield peak. Both the tangent and the secant moduli decrease significantly as strain increases, making it very inaccurate to use the initial modulus for any strain other than zero. The proposed mathematical model (with n constant or variable) provides an efficient means of obtaining the tangent and secant moduli at any point of the stress-strain curve between the origin and the yield peak.